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首页> 外文期刊>Annals of the Institute of Statistical Mathematics >Exact inference for a simple step-stress modelfrom the exponential distribution under time constraint
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Exact inference for a simple step-stress modelfrom the exponential distribution under time constraint

机译：根据时间约束下的指数分布，对简单的阶跃应力模型进行精确推断

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摘要

In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress factors such as temperature, voltage and load on the lifetimes of experimental units. Step-stress test, which is a special class of accelerated life-tests, allows the experimenter to increase the stress levels at fixed times during the experiment in order to obtain information on the parameters of the life distributions more quickly than under normal operating conditions. In this paper, we consider the simple step-stress model from the exponential distribution when there is time constraint on the duration of the experiment. We derive the maximum likelihood estimators (MLEs) of the parameters assuming a cumulative exposure model with lifetimes being exponentially distributed. The exact distributions of the MLEs of parameters are obtained through the use of conditional moment generating functions. We also derive confidence intervals for the parameters using these exact distributions, asymptotic distributions of the MLEs and the parametric bootstrap methods, and assess their performance through a Monte Carlo simulation study. Finally, we present two examples to illustrate all the methods of inference discussed here.
机译：在可靠性和寿命测试实验中，研究人员通常对极端或变化的应力因素（例如温度，电压和负载）对实验单元寿命的影响感兴趣。阶跃压力测试是一类特殊的加速寿命测试，它使实验人员可以在实验过程中的固定时间增加压力水平，以便比正常操作条件下更快地获得寿命分布参数的信息。在本文中，当实验持续时间受到时间限制时，我们将从指数分布考虑简单的阶跃应力模型。我们假设参数的最大似然估计量（MLE）假设寿命是指数分布的累积暴露模型。参数的MLE的确切分布是通过使用条件矩生成函数获得的。我们还使用这些精确分布，MLE的渐近分布和参数自举方法得出参数的置信区间，并通过蒙特卡洛模拟研究评估其性能。最后，我们提供两个示例来说明此处讨论的所有推理方法。

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